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I have no idea my brain is not smart enough to do this. Whoever solves this is truly a genius!!!!!

 

 

A site is any point (x, y) in the plane such that x and y are both positive integers less than or equal to 20.

 

     Initially, each of \(400\) the sites is unoccupied. Amy and Ben take turns placing stones with Amy going first. On her turn, Amy places a new red stone on an unoccupied site such that the distance between any two sites occupied by red stones is not equal to\(\sqrt{5}\). On his turn, Ben places a new blue stone on an unoccupied site. (A site occupied by a blue stone is allowed to be at any distance from any other occupied site.) They stop as soon as a player cannot place a stone.

 

Find the greatest \(K\) such that Amy can ensure that she places at least \(K\) red stones, no matter how Ben places his blue stones

 Feb 20, 2019
edited by CalculatorUser  Feb 20, 2019

Best Answer 

 #1
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See the solution here: https://artofproblemsolving.com/wiki/index.php?title=2018_IMO_Problems/Problem_4

 Feb 20, 2019
 #1
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Best Answer

See the solution here: https://artofproblemsolving.com/wiki/index.php?title=2018_IMO_Problems/Problem_4

Guest Feb 20, 2019

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